The speed of light in this case is better called the speed of causality. So for any 2 objects to be causally connected they cant be further apart than over a given time period than light could travel in that given time period. In other words you cant have a cause and effect relationship between objects that haven’t had time to communicate with each other. If you were on the moon and I shined a laser at you, you couldn’t know that I have done so until the light reaches you.
Information can be inferred as anything that can have this causal relationship.
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